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In magnetic resonance imaging (MRI), accuracy of brain structures quantification may be affected by the partial volume (PV) effect. PV is due to the limited spatial resolution of MRI compared to the size of anatomical structures. When considering the cortex, measurements can be even more difficult as it spans only a few voxels. In tight sulci areas, where the two banks of the cortex are in contact, voxels may be misclassified. The aim of this work is to propose a new PV classification-estimation method which integrates a mechanism for correcting sulci delineation using topology preserving operators after a maximum a posteriori classification. Additionally, we improved the estimation of mixed voxels fractional content by adaptively estimating pure tissue intensity means. Accuracy and precision were assessed using simulated and real MR data and comparison with other existing approaches demonstrated the benefits of our method. Significant improvements in GM classification were brought by the topology correction. The root mean squared error diminished by 6.3% (p < 0.01) on simulated data. The reproducibility error decreased by 9.6% (p < 0.001) and the similarity measure (Jaccard) increased by 3.4% on real data. Furthermore, compared with manually-guided expert segmentations the similarity measure was improved by 12.0% (p < 0.001).